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Differences Between the Traditional CPI and the Chained CPI

Posted by Rob McClelland on

April 19, 2013

Yesterday my colleague Jeffrey Kling testified about issues related to indexing Social Security, other federal programs, and the tax code for inflation. In this post I discuss differences between the traditional consumer price index (CPI) and an alternative index, the chained CPI, that were covered in that testimony.

Inflation—a general increase in the prices of goods and services—can be measured in various ways. Traditionally, the rate of inflation has been computed by multiplying the percentage price change for each item that people purchase by that item’s share of consumer spending in a period before the prices changed and then adding up those changes for all items. But the actual growth in the cost of living—the amount of additional resources that someone would need to maintain the same standard of living this year as last year in the face of rising prices—is generally lower than the rate of inflation when measured that way. The reason for the difference is that many people can lessen the impact of inflation on their standard of living by purchasing fewer goods or services that have risen in price and, instead, buying more goods or services that have not risen in price or have risen less.

How people substitute one good for another when prices change generally depends on the change in the relative prices of the goods (whether one item is becoming more or less expensive relative to another) rather than on the absolute price levels of the two goods (whether one item is more or less expensive than another). The importance of changes in relative prices in consumer decision making means that people do not necessarily shift to lower-priced goods. If the price difference between two items narrows, consumers will tend to buy more of the more expensive one. A common example involves hamburger and steak. If the prices of both items rise, consumers will shift their spending toward the one whose price rises by a smaller percentage: If the price of hamburger increases more than the price of steak does, people will purchase more steak.

To be sure, increases in the general price level that exceed increases in income and wealth lower consumers’ standard of living. But the resulting decline in their standard of living is usually smaller than it would be if substitution were not possible. Thus, measures of inflation that do not account for such substitution overstate growth in the cost of living—a problem known as substitution bias.

The Traditional CPI

Two versions of the CPI are currently used to index federal programs: the consumer price index for all urban consumers (CPI-U) and the consumer price index for urban wage earners and clerical workers (CPI-W). The methodology used by the Bureau of Labor Statistics (BLS) to calculate those indexes suffers from at least two drawbacks—substitution bias and small-sample bias. Both of those drawbacks cause those traditional versions of the CPI to grow more quickly than the chained CPI-U, an improved measure of overall inflation developed by BLS that is discussed below. Substitution bias has been recognized by economists for many years; small-sample bias has also been known for some time, but until recently, it has received little attention. (For more on small-sample bias, see BLS research here and here.)

The traditional versions of the CPI are based on spending patterns from a point in the past, and so do not fully incorporate the effects of consumers’ substitution between various goods and services when their relative prices change. As a result, those traditional versions of the CPI overstate the amount by which consumers’ well being declines when prices rise and understate the benefit of reductions in prices. Therefore, the traditional versions tend to grow faster than the cost of living does.

The traditional versions of the CPI also suffer from a statistical bias that occurs because the index is calculated using prices for only a small portion of the items in the economy. BLS produces an inflation index for an item in a specific region—such as cheese in the Kansas City area—by averaging the growth rates of a sample of prices for that item in that locale. BLS then computes the geometric average of the change in those prices. When the sample of prices is large, the expected value of the geometric average of the price changes in that sample is very close to—but slightly higher than—the geometric average of all price changes for that item in that region. When the sample size is smaller, that upward bias is larger.

BLS creates the item-area indexes using, on average, prices of only about 10 examples of an item. Such a small sample creates a measurable upward bias in those indexes. Because the traditional CPI is calculated as an arithmetic average of those indexes (and the arithmetic average is unbiased), any bias contained in the item-area indexes carries through to the overall CPI.

The Chained CPI-U

BLS has developed another approach to measuring price increases that avoids both substitution bias and small-sample bias. Since August 2002, BLS has published an alternative index, the chained CPI-U, which attempts to account for the effects of substitution on changes in the cost of living. The chained CPI-U provides a more accurate estimate of changes in the cost of living from one month to the next by using market baskets from both months, thus “chaining” the two months together.

The chained CPI-U is also largely free of small-sample bias because of the way in which it is computed. Both the traditional CPI and the chained CPI-U are based on the same item-area indexes, which are calculated using a geometric average. To combine those indexes into an overall estimate of price growth in the United States, however, BLS uses a geometric-average formula for the chained CPI-U, as opposed to an arithmetic average formula for the traditional CPI. The use of a geometric-average formula to combine the item-area indexes effectively makes the number of elements in the geometric average much larger, which essentially eliminates small-sample bias.

The chained CPI-U results in lower estimates of inflation than the traditional CPI does. CBO expects that annual inflation as measured by the chained CPI-U will be about 0.25 percentage points lower, on average, than annual inflation as measured by the traditional CPI. That estimate is based in part on the observed past differences between the chained CPI-U and the traditional CPI-U and CPI-W.

The difference has generally been smaller when overall inflation has been lower—perhaps reflecting fewer increases in the relative prices of goods and services for which consumers spend a great deal and less interest by consumers in substituting between goods and services when price increases are mostly smaller. In addition, the gap between the traditional and the chained CPI-U has generally been smaller when prices for energy have been declining and larger when those prices have been rising rapidly.

Although many analysts consider the chained CPI to be a more accurate measure of the cost of living than the traditional CPI, using it for indexing could have disadvantages. The values of the chained CPI are revised over a period of several years, so affected programs and the tax code would have to be indexed to a preliminary estimate of the chained CPI that is subject to estimation error. Also, the chained CPI may understate growth in the cost of living for some groups, as discussed in another blog post today.